publication . Preprint . 2005

Truncated Groebner fans and lattice ideals

Lauritzen, Niels;
Open Access English
  • Published: 11 Sep 2005
Abstract
We outline a generalization of the Groebner fan of a homogeneous ideal with maximal cells parametrizing truncated Groebner bases. This "truncated" Groebner fan is usually much smaller than the full Groebner fan and offers the natural framework for conversion between truncated Groebner bases. The generic Groebner walk generalizes naturally to this setting by using the Buchberger algorithm with truncation on facets. We specialize to the setting of lattice ideals. Here facets along the generic walk are given by unique (facet) binomials. This along with the representation of binomials as integer vectors give an especially simple version of the generic Groebner walk....
Subjects
arXiv: Computer Science::Symbolic ComputationMathematics::Commutative AlgebraComputer Science::Mathematical Software
free text keywords: Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, Mathematics - Combinatorics, 13P10
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